The Board of Governors of the Federal Reserve System and the Federal Open Market Committee shall maintain long run growth of the monetary and credit aggregates commensurate with the economy's long run potential to increase production, so as to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates.

Three goals are given, namely:

Maximum employment;

Stable prices; and

Moderate long-term interest rates.

So why is it that many (or even most) writings* usually refer only to the dual mandate, i.e. the first two goals of maximum employment and stable prices? Why do they seem to ignore the third goal of moderate long-term interest rates?

Is it because the third goal is less important? Or perhaps because the third goal somehow follows automatically if the first two are fulfilled?

But wait a minute: None of this sounds like a dual mandate. Rather, it sounds as if Congress has given the Fed three mandates—if not four. Over the years, the mandates were boiled down to two: maximum employment and price stability. And now, some say the central bank can focus on price stability.

2 Answers
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As @Fizz suggests, the moderate long-term interest rates mandate is considered redundant:

Just how is the Fed supposed to serve the national interest with this
strange instrument called monetary policy? Under the terms of the
Federal Reserve Act, as amended, Congress has directed the Fed to
promote “maximum employment, stable prices, and moderate long-term
interest rates.” That sounds like three goals, but the phrase is often
called the Fed’s “dual mandate” because the interest rate objective is
considered redundant. Price stability will almost certainly bring low
long-term interest rates in its wake.

Blinder (2012), noting that Blinder is a former Vice Chairman of the Board of Governors of the Federal Reserve System.

There is a literature that says that not only are there two mandates but that effectively that there are one, there is no real trade off between the two. BLANCHARD and GALÍ (2007) (Real Wage Rigidities and the New Keynesian Mode) criticize this approach, which can be shown to be present only in some models.

From a welfare point of view, the model implies that it is desirable
to stabilize inflation and to stabilize the output gap. Equation (1)
implies that the two goals do not conflict: Stabilizing inflation also
stabilizes the output gap. Thus, for example, in response to an
increase in the price of oil, the best policy is to keep inflation
constant;doing so implies that output remains equal to its natural
level. This property, which we shall call the divine coincidence
contrasts with a widespread consensus on the undesirability of
policies that seek to fully stabilize inflation at all times and at
any cost in terms of output. That consensus underlies the medium-term
orientation adopted by most inflation targeting central banks

Or, said another way:

...[T]hese findings suggest that the strong focus on inflation
stabilization by prominent central banks like the ECB is sufficient
for macroeconomic stabilization, and that the focus on resource
utilization in the Fed's mandate is redundant or even harmful.

As for "some say the central bank can focus on price stability" that's an allusion to ECB's primary mandate (sometimes/unofficially called "single mandate"), no doubt.

And hat-tip to BKay for bringing this up, there are indeed more similarities between the Fed and ECB; even though not by law...

As
explained in the 9th edition of the Federal Reserve’s Purposes and Functions, published in
2005: “Stable prices in the long run are a precondition for maximum sustainable output
growth and employment as well as moderate long-term interest rates.” In 2004, Chairman
Greenspan pointed to the primacy of price stability in explaining the success of Federal
Reserve policy since 1979. As he explained, this resulted from “maximizing the probabilities
of achieving our goals of price stability and the maximum sustainable growth that we
associate with it” (Greenspan, 2004).
With this interpretation of the Federal Reserve’s mandate, closer comparison with that of
the ECB suggests more similarities than differences. This is because while the mandate of
the ECB explicitly recognizes the primacy of price stability, it does not ignore other
objectives.

Furthermore, analysis of actual macro models used by the ECB and the Fed (as they were in 2008 anyway) points to a number of "real" similarities, including the fact that neither is strictly IT (Inflation Targeting) in the sense of NCM (New Consensus Macroeconomics)... unlike that of the Bank of England, which was found to be IT.